I worked with phase shift reactions a lot a couple of years ago. I have had some ideas for searching for new phase shift reactions with dr, by basically placing two known oscillator rotors next to each other and seeing if they interact. The project is just complicated enough that I am not particularly motivated to start it at this time, but I thought I would share it here.

The basic idea is to take the rotors of two known oscillators, and find all of the stator cells (both on and off) that must be set in the one-cell boundary around each rotor (calculated via a script). Next put both of these patterns into a dr search, where the rotor/boundary-stator overlaps in any way (accomplished via a script). Finally, set the rotor cells so that they are not counted in the changed-cells total, and only allow for a max of 3 to 4 changed cells. Those 3 to 4 cells would be the stator cells shared by both rotors that interact slightly with each other. Most combinations would probably just terminate due to errors in setting cells, but some would presumably find minor interactions or phase shift reactions.

One concern in this method that may not be obvious at first is that standard dr requires you to set a stable background for each of the rotors, so errors could be caused by choosing "the wrong background" when another choice of background would work. The "don't-check" cells I added might be a remedy to this, but I'm not sure if they wouldn't cause some other unforeseen problem.

I imagine that this method could find phase shift reactions that wouldn't occur naturally or that aren't obviously seen by hand. For example, such a search could probably find this p24 that Dean Hickerson found:

One difficulty in this project might be in choosing which rotors to use. Generally, small rotors and rotors that only change "a little bit" from generation to generation are probably the best for phase shifts. Still, larger rotors would probably be necessary to be the "support" for the phase shift reaction.

Most interesting is the possibility of mutually-phase shifting rotors. This occured naturally in the following p17:

It is only off by one cell in generation 6, and again by that same cell in generation 19.

Also, here is a table of phase shift reactions that I was working on two years ago (Edit: a tub next to a number means that the reaction cannot be accomplished with sub-periodic components, which is obvious for prime periods, but less than obvious for many composite periods):

This table is missing a few notable reactions, such as the 7n+3 given in Dean Hickerson's post linked above, as well as the 4n+1 and 3n+1 reactions represented by these p21 and p22 oscillators respectively:

And wow... That phase-shifter collection is very comprehensive.
Just two things:
- in the 7n+1 column, the p29 is not p29 but actually p141=47*3=7*20+1 (as in jslife), as the sparker is p47.
- There is a p92 = 7 * 13 + 1 in jslife which uses the twin bee shuttle.

EDIT: question regarding your almost p19: I can see that you are phase-shifting both the p7 and the p10... I recognize the 7n-1 reaction, but is the p10 phase-shifting reaction known?

EDIT2: Here's a cute p5 = 4n+1 one I found some time ago... and a 3n+1 reaction.

Scorbie wrote:Here's one from randomagar but it's really cute: Four p4s hassle each other to form a p5:

I only included periods up to 50 in my table. Most phase shift oscillators are based on billiard tables, so high periods are hard to achieve.

By the way, the 6n+8 and 7n-1 reactions were found by Noam Elkies, the 7n+1 reaction was found by Dean Hickerson, and the 5n+2 and 8n+1 reactions were found by myself (based on the p17 oscillator). The 8n+2 and 9n+1 reactions are the same as the 8n+1 reaction.

Scorbie wrote:question regarding your almost p19: I can see that you are phase-shifting both the p7 and the p10... I recognize the 7n-1 reaction, but is the p10 phase-shifting reaction known?

Notice that two phase shifts occur on both rotors. On the burloaferimeter rotor, the phase shift is the standard 7n-1 reaction applied twice. On the p10 rotor, there are two distinct phase shifts: 10n-2 and 10n+1. I'm not sure if these reactions were recognized before, but the following p11 is essentially the p10 phase shifting itself using the 10n+1 reaction:

The interaction in generation 1 causes the phase shift, but notice that there is another interaction in generation 8. Luckily, this second interaction doesn't really affect the oscillator.

JLS was very helpful in this case. I noticed when working by hand that a p7 applied to the p10 would need to interact a second time, which usually means that the pattern will fall apart. In spite of this, I decided to put it into JLS to see if I could get something with no inconsistencies, which succeeded after a fair amount of fiddling.

Very fascinating to see all of the phase-shifting going on. I personally don't like the looks of the p7 and the p10, but I have to admit that they are really versatile in phase-shifting.
1. One thing to note is that the phase-shifting thing is more complex than mere additions and subtractions. After the "hit" the oscillator goes through intermittent states unequal to any of the states in the normal cycle. When the "hit" is given again, then other non-trivial phase-shifting may occur. I can't think of any oscillator based on complex phase-shifting, though.
2. There are so many complex things you can do with this and I can't really think of a way to explore all the possible ways to "hit" an oscillator...
3. The phase-shifting business is really successful with numerous new high-period oscillators! Congrats!

I've never noticed this variant before! It's very clever. It could potentially allow for a p18 oscillator by using the 10n+1 (now 17n+1) reaction from earlier, but I haven't yet found a suitable p9. The single-engine p17 does not allow a p9 support for the p18.

Here's an idea: put this oscillator into a 180-degree symmetric dr search. With luck, we might find something similar to the following p11 signal injector:

The cute p5 I introduced before can actually be seen as a burloaferimeter phase-shifted at 7n-2 (n=1 in this case)
(Of course it can be see as a p4+1 as I said originally)
Edit: Used a phase that occurs in all of the p4, p5, and p7.

Thanks a lot, Bullet51 and BlinkerSpawn!
I have thought of several use cases of this oscillator way before, but now I can't think of any... Will come back for more.
Here's a p6 wick, found by me and stabilized by hought99:viewtopic.php?f=2&t=576&p=24767&hilit=p7+domino#p24408

Edit: @Bullet51 and that's a pretty pretty reaction right there! Looks as if the t-tetromino should move somewhere but it stays the same. Cool.

Edit2 @gmc_nxtman Thanks!!! Yeah, and I was quite surprised before when there was a very sparky p7 pipsquirter but there wasn't a p7 HW emulator...

Last edited by Scorbie on December 17th, 2016, 2:31 pm, edited 2 times in total.